The consecutive even integers are 4,6 and 8.
What are the consecutive even integers?An even number is a number that can be perfectly divided by 2. An example of an even number is 10. A consecutive even number is an even number that follows each other on the number line.
Let the first even number be represented with x
The second even number : x + 2
The third even number : x + 4
x + 2(x + 4) = 20
x + 2x + 8 = 20
3x = 20 - 8
3x = 12
x = 12 / 3
x = 4
The second even number : 4 + 2 = 6
The third even number : 4 + 4 = 8
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A grain silo has a cylindrical shape. Its diameter is 17 , and its height is 38. What is the volume of the silo?
The volume of the silo of cylinder shape containing grain is 8625.24 cubic units.
The volume of the cylindrical shaped grain silo will be calculated by the formula -
Volume = πr²h, where r represents radius and h represents height of the cylinder.
Now, as we know radius is half of the diameter. So, radius = 17/2
Performing division on Right Hand Side of the equation
Radius of the cylinder = 8.5
Keep the values in formula to find the value of volume of silo
Volume = π × 8.5² × 38
Taking square and performing multiplication on Right Hand Side of the equation
Volume = 8625.24 cubic units
Hence, the volume is 8625.24 cubic units.
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in the country of united states of heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.6 inches, and standard deviation of 6.5 inches. a) what is the probability that a randomly chosen child has a height of less than 40.65 inches? answer
The probability that a randomly chosen child has a height of less than 68.15 inches is 0.9162, the probability that a randomly chosen child has a height of more than 54.4 inches is 0.6255.
Simply put, probability is the liability that commodity will do. When we do not know how an event will turn out, we can bandy the liability or liability of several issues. Statistics is the study of events that follow a probability distribution.
a) We need to find p(x<68.15)
Standardize x to z, we have, z = (68.15-μ)/σ
=(68.15-57)/8.1
=1.38
Reading from standard normal tables,
p(z<1.38) =0.9162.
Therefore, the probability that a randomly chosen child has a height of less than 68.15 inches is 0.9162.
b) We need to find p(x>54.4)
Standardize x to z, we have, z = (54.4-μ)/σ
=(54.4-57)/8.1
=-0.32
Reading from standard normal tables,
p(z>-0.32) = 0.6255
Therefore, the probability that a randomly chosen child has a height of more than 54.4 inches is 0.6255.
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A bathtub containing 42 gallons of water is draining at a constant rate. After 2 minutes, it holds 30 gallons of water. Write an equation that represents the number y of gallons of water in the tub after 2 minutes.
Answer:
30.
Step-by-step explanation:
We can write an equation for the number of gallons of water in the bathtub using the rate of change (drainage) and the elapsed time. Let y be the number of gallons of water in the tub after t minutes. Then, the equation can be written as:
y = 42 - (drainage rate) * t
Since we know that after 2 minutes, the tub holds 30 gallons of water, we can use this information to solve for the drainage rate:
30 = 42 - (drainage rate) * 2
12 = (drainage rate) * 2
drainage rate = 6 gallons per minute
Substituting this value into the original equation, we get:
y = 42 - 6t
So, the equation that represents the number of gallons of water in the tub after 2 minutes is:
y = 42 - 6 * 2 = 42 - 12 = 30.
Answer:
The equation representing the number of gallons of water in the tub after t minutes can be represented by a linear function y = mx + b, where y is the number of gallons of water, x is the number of minutes, m is the rate of change (or the slope) and b is the y-intercept.
Since the bathtub is draining at a constant rate, the slope (m) can be found by finding the difference between the initial number of gallons of water (42) and the number of gallons after 2 minutes (30), and dividing by the difference in time (2 minutes):
m = (42 - 30) / 2 = 6 gallons per minute
The y-intercept (b) can be found using the initial conditions of the problem, when t = 0:
b = 42 - (6 * 0) = 42
Therefore, the equation representing the number of gallons of water in the tub after t minutes can be written as:
y = 6t + 42
So, after 2 minutes, y = 6 * 2 + 42 = 54 gallons of water.
f(x) = -x² + 5 and g(x) = -2x+2, find all values of x for which f(x) = g(x).
Answer: Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).
Step-by-step explanation:
To find all values of x for which f(x) = g(x), we can set the two functions equal to each other and solve for x:
-x² + 5 = -2x + 2
Expanding the right-hand side:
-x² + 5 = -2x + 2
-x² + 2x + 3 = 0
Solving for x using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 2, and c = 3
x = (-2 ± √(2² - 4(1)(3))) / 2(1)
x = (-2 ± √(4 - 12)) / 2
x = (-2 ± √(-8)) / 2
Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).
12. Solve the problem.
According to a college survey, 22% of all students work full time. Find the mean for the
number of students who work full time in samples of size 16.
00.2
03.5
04.0
02.8
The mean for the number of students who work full-time in
samples of size 16 are 3.5.
What is the expected value?We understand The expected value, also known as the expected average in the field of probability theory, is a generalization of the weighted average.
Given, 22% of all students work full-time, per a college poll.
Now, If we choose a sample of 16 students the mean number of students working full-time is,
= 16(22/100)
= 16×0.22
= 3.5.
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Determine each segment length in right triangle ABC . Right triangle ABC with right angle at vertex B. Point D lies on side AC. Dashed segment BD is drawn. Angle BAD measures 30 degrees and angle BCD measures 60 degrees. Angle BDC is a right angle. Side AC is labeled 8 and segment CD is labeled 2. 2 2 4 3 6 4 2 2 3 4 B C arrowRight A D arrowRight A B arrowRight B D
The right triangle ABC with right angle at vertex B has the length of the segment is; 4√2 unit.
What is Pythagorean theorem?The Pythagorean theorem state that in any right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the two shorter sides. In this case, side AC is the hypotenuse and side AB and BC are the two shorter sides.
We can find the lengths of all three sides using the Pythagorean theorem and the information given. Side AB is equal to the square root of the sum of the squares of sides AC and BC. Since we are given that angle ABC is a right angle, we can find that side BC is equal to the length of side AB.
The side lengths are 8/2 = 4
Now, Another side length that is x
So , the equation formed is;
xcos45 = 4
x/√2 = 4
x = 4√2
Hence the length of the segment is; 4√2 unit.
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Mrs. Harris has a piece of lumber that is 11 5/8 inches wide she plans to split the width of the lumber into three equal pieces how wide will each piece be
The size of width of each lumber piece will be 3.875 inches.
What is Algebra?Logic is the arrangement of all those concepts, whereas algebra is the study of abstract concepts.
Making something a little less complicated while both making it easier to attain or understand is the concept of clarity.
Mrs. Harris intends to divide the breadth of a piece of timber that is 11 ⁵/₈ inches broad into three equal pieces.
Convert the mixed fraction number to a decimal number. Then we have
11 ⁵/₈ = 11 + ⁵/₈
11 ⁵/₈ = 11.625 inches
The width of each lumber piece is given as,
⇒ 11.625 / 3
⇒ 3.875 inches
The size of width of each lumber piece will be 3.875 inches.
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Find b and then solve the equation
2x^2+bx-10=0 if one of its roots is 5
well, since we know that one root is 5, that is a factor of it is (x-5), so hmmm by the remainder theorem we also know that if we plug "5" as our argument in our f(x), that is, if we do f(5), it must result to 0. so f(5) = 0, if that's so then
[tex]2x^2+bx-10=f(x)\implies 2(5)^2+b(5)-10=f(5) \\\\\\ 2(5)^2+b(5)-10=0\implies 50+5b-10=0\implies 5b=-40 \\\\\\ b=\cfrac{-40}{5}\implies \boxed{b=-8} \\\\[-0.35em] ~\dotfill\\\\ 2x^2-8x-10=0\implies 2(x^2-4x-5)=0\implies 2\stackrel{ {\Large \begin{array}{llll} x=-1 \end{array}} }{(x+1)}(x-5)=0[/tex]
Groundhog Day predictions have a 39% accuracy. How baby times should we expect to be correct over the next 38 years? *PLEASE HELP*
It would be expected to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.
What is the expected value?The expected value, also known as the mathematical expectation, is a key concept in probability theory and statistics.
Here,
Groundhog Day predictions have a 39% accuracy, so on average, 39% of the predictions made on Groundhog Day are correct.
To find the expected number of correct predictions over the next 38 years, we can multiply the accuracy of the predictions (39%) by the number of predictions made (38),
39% * 38 = 14.82
So, we would expect to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.
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One way of writing 75 as the sum of consecutive whole numbers is 24 + 25 + 26. How many other ways are there?
Answer:
None. [tex]24+25+26[/tex] is the only valid answer
Step-by-step explanation:
We can create an expression for the sum of 3 consecutive numbers.
[tex]S=x+(x+1)+(x+2)[/tex]
Which we can simplify to
[tex]S=x+x+1+x+2[/tex]
[tex]S=3x+3[/tex]
In this example we are given a sum of 75.
[tex]75=3x+3[/tex]
Lets solve for [tex]x[/tex].
Subtract 3 from both sides.
[tex]72=3x[/tex]
Divide both sides by 3.
[tex]24=x[/tex]
To find out what the 3 numbers are we can plug in 24 for x
[tex]x+(x+1)+(x+2)[/tex]
[tex]24+(24+1)+(24+2)[/tex]
[tex]24+25+26[/tex]
Answer:
4 other ways (5 ways, total).
Step-by-step explanation:
You want to know how many other ways 75 can be written as the sum of consecutive whole numbers other than 24+25+26.
SolutionIf 75 is written as the sum of an odd number of integers, the middle integer of the set will be 75 divided by the number of integers. The divisors of 75 are {1, 3, 5, 15, 25, 75}. If the numbers in the sum are non-negative, the number of integers involved cannot be more than √(2·75) ≈ 12. Then allowed odd numbers of integers in the sum are 3 and 5.
If 75 is written as the sum of an even number of integers, the quotient when 75 is divided by the number of integers must be 1/2 more than a whole number. Such integer divisors are 2, 6, and 10.
Sums37 + 38 = 75 . . . . 2 integers
24 + 25 + 26 = 75 . . . . 3 integers (the given sum)
13 + 14 + 15 + 16 + 17 = 75 . . . . 5 integers
10 + 11 + 12 + 13 + 14 + 15 = 75 . . . . 6 integers
3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 75 . . . . 10 integers
There are 4 other ways to use consecutive non-negative integers to make a sum of 75.
What is x and y equal to?
-10x + 4y = -14
7x + 5y = 2
Answer: x =1, y = -1
Step-by-step explanation:
-10x+4y=-14
7x+5y=2
Let's eliminate y.
5(-10x+4y= -14)
4(7x + 5y=2)
[ I multiplied the first equation by the coefficient of y in the second equation and did the same in the second equation].
=> -50x+20y =-70
28x+20y = 8
Notice how the coefficients of y are the same. We can subtract the 2 equations to eliminate y.
Thus,
-78x = -78 ( y has been eliminated)
∴ x=-78/-78 =1.
Put the value of x in any equation to find y.
7x + 5y =2
=> 7(1) + 5y =2
7+5y=2
5y = 2-7
5y = -5
y = -1.
Hope this helps :)
is this true or false? f (n )equals o (g (n ))space a n d space g (n )equals omega (h (n ))space t h e n space f (n )equals theta (h (n ))true false
The statement "If f(n) = O(g(n)) and g(n) = Ω(h(n)), then f(n) = Θ(h(n))" is actually true.
This can be proven using the formal definitions of the O-notation, Ω-notation, and Θ-notation:
f(n) = O(g(n)) means that there exist positive constants c and n0 such that |f(n)| ≤ c|g(n)| for all n ≥ n0.
g(n) = Ω(h(n)) means that there exist positive constants c' and n0' such that |g(n)| ≥ c'|h(n)| for all n ≥ n0'.
f(n) = Θ(h(n)) means that there exist positive constants c1, c2, and n1 such that c1|h(n)| ≤ |f(n)| ≤ c2|h(n)| for all n ≥ n1.
If we assume that f(n) = O(g(n)) and g(n) = Ω(h(n)), we can use the definitions above to show that f(n) = Θ(h(n)).
Since g(n) = Ω(h(n)), we have |g(n)| ≥ c'|h(n)| for some positive constants c' and n0', and since f(n) = O(g(n)), we have |f(n)| ≤ c|g(n)| for some positive constants c and n0.
Combining these two inequalities, we get:
|f(n)| ≤ c|g(n)| ≤ c(c'/c)|h(n)|
Therefore, f(n) = Θ(h(n)) with constants c1 = 1 and c2 = c(c'/c), and n1 = max(n0, n0').
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how many ways can patricia choose 3 pizza toppings from a menu of 10 toppings if each topping can only be chosen once?
Step-by-step explanation:
the equation we use here is [items to choose from] to the power of [required items]; in this case, we get [tex]10^{3}[/tex].
HELP will give BRAINLYST
Can anyone help me with this? I’ll give brainliest and 20 points
Based on the Venn diagram, the number of people in each set are follows:
A∩B = 11 peopleThe number of people in A alone = 13The number of people in B alone = 19What is the number of people in each set in the Venn diagram?The number of people in each set in the Venn diagram is calculated as follows:
The universal set has a total of 50 people
Let the intersection of A and B be x
A∩B = x
The number of people in A alone = 24 - x
The number of people in B alone = 30 - x
x + (24 - x) + (30 - x) + 7 = 50
61 - x = 50
x = 61 - 50
x = 11
A∩B = 11
Hence;
The number of people in A alone = 24 - 11
The number of people in A alone = 13
The number of people in B alone = 30 - 11
The number of people in B alone = 19
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34 on april 18, 1775, paul revere set off on his midnight ride from charlestown to lexington. if he had ridden straight to lexington without stopping, he would have traveled 11 miles in 26 minutes. in such a ride, what would the average speed of his horse have b
The average speed of Paul Revere's horse, assuming he rode straight to Lexington without stopping, would have been approximately 25.4 miles per hour.
To find the average speed of Paul Revere's horse, we can use the formula:
average speed = total distance / total time
In this case, the total distance is 11 miles, and the total time is 26 minutes, or 0.4333 hours (since there are 60 minutes in an hour).
So, the average speed of Paul Revere's horse would be:
average speed = 11 miles / 0.4333 hours
average speed ≈ 25.4 miles per hour
Therefore, the average speed of Paul Revere's horse, to the nearest tenth of a mile per hour, would have been 25.4 miles per hour.
Using the formula for average speed, we can calculate that Paul Revere's horse would have had to travel at an average speed of approximately 25.4 miles per hour to cover the 11-mile distance in 26 minutes. This assumes that he rode straight through without stopping.
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The complete question is:
On April 18, 1775, Paul Revere set off on his midnight ride from Charlestown to Lexington. If he had ridden straight to Lexington without stopping, he would have traveled 11 miles in 26 minutes. In such a ride, what would the average speed of his horse have been, to the nearest tenth of a mile per hour?
Please need help with this math problem
Answer:
maximum value = 135
Step-by-step explanation:
the maximum value is situated at the right end of the whisker.
each division on the number line is 5 units
so maximum value = 125 + 2 units = 125 + 10 = 135
A candle burns 2 inches per hour. After burning for 2 hours, the candle was 5 inches
long. If one the candle has been burning for 240 minutes, how long is the candle?
Write an equation that models the situation.
The length of the candle that has been burning for the total of 240 minutes would be = 9 inches.
How to calculate the length of the candle?The rate at which a candle burns = 2 in/ 2 hours
That is,
2 in = 2 hour; 2 inches = 120 minutes
X in = 240 minutes
Make X the subject of formula;
X = 2×240/120
X= 480/120
X = 4+5
X = 9 inches
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Write the linear equation given slope is -1/3 and the point (-9,-1)
The Linear Equation for the line with slope as -1/3 and the point (-9,-1) is y = (-1/3)x - 4 .
We use the point slope form of a linear equation to write the equation of a line with its slope and a point on the line.
The point-slope form is ⇒ y - y₁ = m(x - x₁) ;
Where m is = slope of line, and (x₁, y₁) is a point on line.
The Slope (m) of line is = -1/3 and point on line (x₁, y₁) is = (-9, -1),
Now , we substitute these values ;
we get ;
⇒ y - (-1) = (-1/3)(x - (-9)) ;
⇒ y + 1 = (-1/3)(x + 9) ;
Simplifying further ,
we get ;
⇒ y + 1 = (-1/3)x - 9/3 ;
Subtracting 1 from both sides, we get:
⇒ y = (-1/3)x - 4
Therefore, the equation of the line is y = (-1/3)x - 4 .
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HELP ME PLEASE ASAP! I NEED TO PASS THIS CLASS BY MONDAY!
The length of the two sides of the given right triangle is 5√2
What is a right triangle?A triangle with an angle right angle is called a right triangle.
Given that, a right triangle, with an acute angle of 45° and the length of hypotenuse is 10 units,
We need to find the length of two sides u and v,
The sum of a triangle is 180°, and if one angle is 90° and the other is 45° therefore, the third is also 45°
Now, we know that, sides opposite to equal angles are equal,
Therefore, v = u,
Now, using the Pythagoras theorem,
10² = v²+u²
v² + v² = 100
2v² = 100
v² = 50
v = 5√2
u = 5√2
Hence, the length of the two sides of the given right triangle is 5√2
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So I have to solve for x here: x/4 - 6 = x/12 + 2
Answer:
X = 48
Step-by-step explanation:
x/4 - 6 = x/12 + 2
= 3x-72=x+24
= 3x=x+96
= 2x=96
= x=48
Answer:
x=48
Step-by-step explanation:
You can solve by x by simplifying both sides of the equation, then isolating the variable
What is the area of this compound figure?
Answer:
199 cm²
Step-by-step explanation:
in the picture
a bag of 15 scrabble tiles contains three each of the letters a, c, e, h, and n. if you pick six letters one at a time, what is the chance that you spell c-h-a-n-c-e?
A bag of 15 scrabble tiles contains three each of the letters a, c, e, h, and n. The chance of spelling "chance" is approximately 0.0108 or about 1.08%.
First, we need to count the number of ways to choose two "c"s, two "e"s, and one each of "h" and "n" from the 15 tiles in the bag. To do this, we use the combination formula:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of items and r is the number of items we want to choose. For example, to choose two "c"s from three, we can calculate:
C(3, 2) = 3! / (2! * (3 - 2)!) = 3
We can use this formula to calculate the number of ways to choose two "c"s, two "e"s, and one each of "h" and "n":
C(3, 2) * C(3, 2) * C(3, 1) * C(3, 1) = 54
Therefore, there are 54 ways to choose the required letters out of the 15 tiles in the bag.
Next, we need to count the total number of ways to choose 6 tiles from the 15 in the bag. We can again use the combination formula:
C(15, 6) = 15! / (6! * (15 - 6)!) = 5005
Therefore, there are 5005 ways to choose any 6 tiles from the bag.
Finally, we can calculate the probability of spelling "chance" by dividing the number of ways to choose the required letters by the total number of ways to choose 6 tiles:
54 / 5005 ≈ 0.0108 or about 1.08%
So the probability of spelling "chance" when picking six tiles one at a time from the bag is approximately 0.0108 or about 1.08%.
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SOLVING EQUATIONS Solve the equation. Check your solution.
50. y+4-1 = 18
52. v-7= 9+12
St 53.5+44=2+r
51. m+ 18+ 23 = 71
54. 22 +15=d-17
The solution of the equation are as follows:
y = 15
v = 28
r = 95.5
m = 30
d = 54
How to solve equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =. The equation can be solved by finding the value of the variables.
A variable is a number represented with letter in an equation.
Therefore, let's solve the equation.
y + 4 - 1 = 18
y = 18 - 4 + 1
y = 15
v - 7 = 9 + 12
v = 12 + 9 + 7
v = 28
53.5 + 44 = 2 + r
r = 53.5 + 44 - 2
r = 95.5
m + 18 + 23 = 71
m = 71 - 18 - 23
m = 30
22 + 15 = d - 17
d = 22 + 15 + 17
d = 54
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Pls help thank you will mark the Brainliest
Option d) [tex]y= 30.5(0.7)^x[/tex] is the function that best models the number of game systems sold in millions x years since 2015.
Describe Function?In mathematics, a function is a rule that associates each element in one set (called the domain) with a unique element in another set (called the range). The rule specifies how the input values (the elements of the domain) are transformed into output values (the elements of the range).
A function can be represented using various notations, such as f(x), where f is the name of the function and x is the input value, or y = f(x), where y is the output value and x is the input value. The function can be defined explicitly, as in[tex]f(x) = x^2,[/tex] or implicitly, as in the equation of a circle, [tex]x^2 + y^2 = r^2[/tex], where y is a function of x.
To determine which function best models the number of game systems sold, we need to observe the trend in the data.
We can see that the number of game systems sold is decreasing as time goes on, which means the function should be decreasing as well.
Option a) [tex]y=21.35(0.7)^x[/tex] is an exponential function with a base less than 1, which means it would also be decreasing. However, it starts with a higher initial value than the data suggests.
Option b) [tex]y= 30.5(21.35)^x[/tex] is an exponential function with a base greater than 1, which means it would be increasing. This function does not match the trend in the data.
Option c) [tex]y= 30.5(1.3)^x[/tex] is an exponential function with a base greater than 1, which means it would be increasing. This function also does not match the trend in the data.
Option d) [tex]y= 30.5(0.7)^x[/tex]is an exponential function with a base less than 1, which means it would be decreasing. Additionally, this function passes through all three data points, and it has a starting value that matches the first data point. Therefore, option d) is the function that best models the number of game systems sold in millions x years since 2015.
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Someone help me with this equation please!!
The given statement is transitive property.
What is transitive property?Transitive property is also called transitive property of equality when we have two equal values and either of this value is equal to third value.
DE≅XY AND [tex]\hat{DE}$$\approx\hat{XY} and \hat{XY}$$\approx$$\YZ, then\hat{DE}$$\approx$$\hat{YZ}[/tex]
This is a transitive property.
Here we have three values, initially first two values are equal and second & third values are equal.
Which gives any one of the value of first and second equals third value.
This is the transitive property.
Hence, the given statement is transitive property.
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Feb 10, 9:11:47 AM
10. Find the value of X.
The solution of x in the rhombus is 3
How to determine the solution of x in the shapeFrom the question, we have the following parameters that can be used in our computation:
The rhombus
Also, we have
LN = 14
AN = x + 4
Using the above as a guide, we have the following equation:
LN = 2 * AN
Substitute the known values in the above equation, so, we have the following representation
2 * (x + 4) = 14
Evaluate the expression
x + 4 = 7
Subtract 4 from both sides
so, we have the following representation
x = 3
Hence, the solution is 3
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the following frequency table represents the number of drinks someone has in a week for 40 people. what is the 70th percentile of the data?
Answer:
Step-by-step explanation:
what is the number of ways to choose two toppings for a pizza, one topping from a group of 5 kinds of meats and the other topping from a group of 7 kinds of vegetables?
There are 35 ways to choose two toppings for a pizza, one topping from a group of 5 kinds of meats and the other topping from a group of 7 kinds of vegetables.
The multiplication rule of counting in Permutation and Combinations states that if there are n ways to perform one task and m ways to perform a second task, then there are n x m ways to perform both tasks in sequence.
The number of ways to choose a meat topping from 5 kinds of meats = 5.
The number of ways to choose a vegetable topping from 7 kinds of vegetables = 7.
Using the multiplication rule, the number of ways to choose one meat topping and one vegetable topping is = 5 x 7 = 35 ways.
Learn more about multiplication rule of counting from the below link:
https://brainly.com/question/15096318
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A coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50%.
